{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# CR Nonconforming Element for Poisson Equation in 3D"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This example is to show the rate of convergence of the CR Nonconforming finite element approximation of the Poisson equation on the unit cube:\n",
    "\n",
    "$$- \\Delta u = f \\; \\hbox{in } (0,1)^3$$\n",
    "\n",
    "for the following boundary conditions\n",
    "- Non-empty Dirichlet boundary condition: $u=g_D \\hbox{ on }\\Gamma_D, \\nabla u\\cdot n=g_N \\hbox{ on }\\Gamma_N.$\n",
    "- Pure Neumann boundary condition: $\\nabla u\\cdot n=g_N \\hbox{ on } \\partial \\Omega$.\n",
    "- Robin boundary condition: $g_R u + \\nabla u\\cdot n=g_N \\hbox{ on }\\partial \\Omega$.\n",
    "\n",
    "**References**:\n",
    "- [Quick Introduction to Finite Element Methods](femdoc.html)\n",
    "- [Introduction to Finite Element Methods](http://www.math.uci.edu/~chenlong/226/Ch2FEM.pdf)\n",
    "- [Progamming of Finite Element Methods](http://www.math.uci.edu/~chenlong/226/Ch3FEMCode.pdf)\n",
    "\n",
    "**Subroutines**:\n",
    "\n",
    "    - Poisson3CR\n",
    "    - cubePoisson\n",
    "    - femPoisson3\n",
    "    - Poisson3CRfemrate\n",
    "    \n",
    "The method is implemented in `Poisson3CR` subroutine and tested in `cubePoissonCR`. Together with other elements (P1,P2,Q1,WG,CR), `femPoisson3` provides a concise interface to solve Poisson equation. The CR element is tested in `Poisson3CRfemrate`. This doc is based on `Poisson3CRfemrate`.    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## CR Nonconforming Element\n",
    "\n",
    "We explain degree of freedoms and basis functions for Crouzeix-Raviart nonconforming P1 element on a tetrahedron. The dofs are associated to faces. Given a mesh, the required data structure can be constructured by\n",
    "\n",
    "    [elem2face,face] = dof3face(elem);\n",
    "      \n",
    "### Local indexing      "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "node = [0,0,0; 1,0,0; 0,1,0; 0,0,1];\n",
    "elem = [1 2 3 4];\n",
    "face = [2 3 4; 1 3 4; 1 2 4; 1 2 3];\n",
    "showmesh3(node,elem); view([-26 10]);\n",
    "findnode3(node);\n",
    "findelem(node,face);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A Local Basis\n",
    "\n",
    "The 4 Lagrange-type bases functions are denoted by $\\phi_i, i=1:4$, i.e. $\\phi_i(m_j)=\\delta _{ij},i,j=1:4$, where $m_i$ is the center of the i-th face. In barycentric coordinates, they are:\n",
    "\n",
    "$$\\phi_i = 1- 2\\lambda_i,\\quad \\nabla \\phi_i = -2\\nabla \\lambda_i,\\quad i =1:4.$$\n",
    "\n",
    "When transfer to the reference triangle formed by $(0,0,0),(1,0,0),(0,1,0),(0,0,1)$, the local bases in x-y-z coordinate can be obtained by substituting \n",
    "\n",
    "$$\\lambda _1 = x, \\quad \\lambda _2 = y, \\quad \\lambda _3 = z, \\quad \\lambda_4 = 1-x-y-z.$$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mixed boundary condition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%% Setting\n",
    "[node,elem] = cubemesh([0,1,0,1,0,1],0.5); \n",
    "mesh = struct('node',node,'elem',elem);\n",
    "option.L0 = 1;\n",
    "option.maxIt = 4;\n",
    "option.elemType = 'CR';\n",
    "option.printlevel = 1;\n",
    "option.plotflag = 1;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Multigrid V-cycle Preconditioner with Conjugate Gradient Method\n",
      "#dof:     6528,  #nnz:    23040, smoothing: (1,1), iter: 17,   err = 7.80e-09,   time =  0.1 s\n",
      "Multigrid V-cycle Preconditioner with Conjugate Gradient Method\n",
      "#dof:    50688,  #nnz:   190464, smoothing: (1,1), iter: 17,   err = 9.10e-09,   time = 0.25 s\n",
      "Multigrid V-cycle Preconditioner with Conjugate Gradient Method\n",
      "#dof:   399360,  #nnz:  1548288, smoothing: (1,1), iter: 17,   err = 9.78e-09,   time =  2.6 s\n",
      "Table: Error\n",
      " #Dof        h        ||u-u_h||    ||Du-Du_h||   ||DuI-Du_h|| ||uI-u_h||_{max}\n",
      "\n",
      "   864   2.500e-01   1.57877e-02   5.75062e-01   1.15791e-01   1.49758e-02\n",
      "  6528   1.250e-01   4.18680e-03   2.93247e-01   5.28394e-02   4.03690e-03\n",
      " 50688   6.250e-02   1.06111e-03   1.47388e-01   2.58754e-02   1.05299e-03\n",
      "399360   3.125e-02   2.66154e-04   7.37911e-02   1.28726e-02   2.66527e-04\n",
      "\n",
      "Table: CPU time\n",
      " #Dof    Assemble     Solve      Error      Mesh    \n",
      "\n",
      "   864   1.10e-01   7.92e-03   1.00e-01   2.00e-02\n",
      "  6528   5.00e-02   1.02e-01   5.00e-02   1.00e-02\n",
      " 50688   2.10e-01   2.47e-01   2.10e-01   1.00e-01\n",
      "399360   2.42e+00   2.60e+00   1.47e+00   0.00e+00\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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pqf3J7t27i/hGEMSemTNnbt26defOnVlZWZ41QDwABQnxkG3btsXExKSnpwNA\n+/btR4wY8eOPP7IFaceOHYMGDWrXrh0AdOvWrV+/fhs3biwvL7c/iYKESI3BgwenpqauWLGCpmnP\nGiAegIKEeMi5c+diYmKYhzExMSdPnmQ3CA8PP3PmDDmmabq0tPTMmTMURdmf9JvNCMKTRx99FAAK\nCwtPnDjhWQPEA3ANSflYLJbff/+9vLzct93W1tYGBd35QRMUFHT79m12g2eeeebgwYPTp0/ftWvX\n5MmTb968WVVV5fCkbw1D1INAvo2IBQqSYqmpqZk8eXJYWFinTp0SEhLCw8PHjBljsbhXTTo4OPjz\nzz93+FRISEhlZSXzsLKy8p577mE3iIqK2rFjR3Fx8fTp0+Pi4kaOHNmuXTuHJz14d4iaEdq3EbHA\nKTtlUlVVNWDAgJMnT86dOzcjIwMA1q9fP3v27CFDhuzevfv+++/3/hIURbEnK4qKinr06MFucPXq\n1fr6+pUrV5KHKSkpU6ZMcXjSe2MQ9eAH30bEAkdIymTx4sUHDhwoKCh48cUXO3Xq1KlTpylTpixc\nuLC4uPizzz7zySUeffTR6urqjz/+GAAKCwt/+OGHESNGAMCSJUt27NgBAEFBQcOGDTtw4AAAbNq0\n6ejRoyNGjHB40if2ICrBD77tDMa3EYFAQVIgNE3PmTPnqaeeeuihh9jnn3rqqQ8++CAqKsqt3m7d\nujVx4sTw8PC2bdvqdLqbN2+S8/fee+/y5ctnzJjRrl271NRUg8GQnJwMAAaD4ccffwSA1q1bz549\n+5lnnomJiXnhhRfWrFnTsmVLhyd99L4R5eMf33YG49uIUNCqIS4uTkbdesO5c+cAwGw2e99V8+bN\n27dv/8QTTyxfvnzatGnNmzd/88032Q0aGhrOnz9/+/Ztjk4uX77M8yRPhPjMJfg9eoBv34UEPxN/\n+rZEUPx3ygbXkBTIqVOnAKBjx44+6Y2iqPXr1wPAuHHjiouLt2zZwn5Wo9G0b9+euweH0/o41494\ngD99G/E/ihKkioqK559/fu3atSLaUHvpLMezzdrG2JzxVXv7ljZB2B4zatQo5jghIeHgwYM+6RaR\nH1bOZynB2tu1RN9WKgoRpLq6ug8++GDr1q0uZ4GF5kbBN1e/mevs2bhV523OWP6ezNEb//Ztxk5r\nM3YaOdZqtQDgcMPp119/ff78+WnTpnFc1Ab2UEaj0dC4L121LAMwOn/W3i+0nL3xb28EMDQ1Qd9W\nNAoRpICAgMGDB6enp7/66qviWhKaNjY0bSz/9tole9zq31l79ggpOjo6LCxs7dq1L730kk2z999/\nX/oZfxGJkgXgVto29/YFOW9P3TlE31Y2yhGkvn371tfXi22Ig6kz/7cPCAiYDkk5pgAAIABJREFU\nMmXKrFmzfv3110ceeYQ5v2XLlsOHD0+dOtWtKyJII5T47dG3lY1Ew74rKirOnr1rsaS6uvrkyZM3\nbtxgzuzatctgMBgMhi+++MLvBkqdqVOndu7ceciQIR9//PGpU6cuX7785Zdfjh079uGHH9br9eyW\nMirowqag2GkFJpWj+HpIivdtgZBFPSSJjpAWLVpUXl6ek5NDHq5bt27WrFlRUVGlpaWZmZlvvPEG\nAERHR/fv3x8A2rRpI6atkiQsLOy333575ZVXpk2bduvWLQAICAjQ6/U5OTkBAXf9CjGZTFevXjWb\nzeIY6inpS36nwkMMQ7W6JBcxfmpD8fWQFO/bApGdnZ2dnS11TRI77tyW+fPnZ2ZmxsXFMXsCysrK\nevfuvXv3bpqmL1261K9fv507dzp8bV1d3cMPP+ys57gmFi5c6EODJR7XX19ff+zYscOHD1dVVdk8\n9c4776SmpgJAVlaWGKZ5TlxcHLy2hfxR7+3M23ve464WLlzIOIYPLRQLVe1ZUaRv26Oq71RyI6SU\nlJTExMQNGzbQTREve/fujYyMJFkAIiIiMjIytm/fnpKS4kHn0i+Y6HMCAgKcVRuSdUEXXVJ7874L\nAGC9Vq1f8Ydps8Wz0RL52QgAUv/liNihVN9WM5JbQ0pKSurfv39sbCxz5uLFi+ytl5GRkZcuXXL4\n2sDAwF9//VVwE5XCo48+OmzYsK5du4ptiCfkZXa3vJ3CKBCRJe0/d5k2uRvahSgQWfu2mpGcINlT\nV1cXGBjIPAwKCqqtrRXRHkQiUOEhRJaMQxs3sFivVRs3W1CWEESmyECQgoODq6urmYdVVVXBwcEi\n2oNICio8xDBMi7KEIApABoIUHR1ttVqZhxaLpUOHDp51pfiIWNXipSyhYyCIFJCBICUlJdXU1KxY\nsQIAjh49um3btvT0dM+6UnxErMrxWJbQMRBECshAkFq0aDFnzpz58+enpKRkZmZOnjy5T58+YhuF\nSBecxEMQmSKbfII0TV+5ciUsLCwoyMNQ9fj4eCHCvgXqFuGA/2duvVa9bN8F4+Y7OkSFh+j6ts9K\nak+Fh3jWp5Tx7btQxmcid1T1ncpghETQaDQREREeqxGiTpyNltI/2m/aZLFeqwYA0yZLQXGZJeM9\nzbSt2n/uKiguw4EUgoiCuv6/5+bm4mqBCiGylJXUftm+C+bfLlivVRNZMv92gQoLKSgub7bmam2L\nxgRU6Ut+JweGYdzlExAE8TGyGSH5BFQjNUNkKf+VBONQLZmvs16rLiguBwBGjciYCQAGdrlPLDsR\nRLWoS5AQhJGlvMzuNstI7Db6FX/42TAEQVCQEDVChYfoktrnv5Lg8Fkyp+dnkxAEQUFSJjU1NUy5\nQvaxUq/756JXK4/ucvdVVHiIw0GSs/OIFBDLx6RmgyJRlyCpZ0P+oEGDvv/+e/tjRV73Rv43tZfP\nlhqe9kCW8jIdp4t2dh4RHbF8W2o2KBJ1CRIGNSiS0PSxMaZvIyfNJ7JkeSWZvyxtO1VufxKn7BBE\nFNQV9o0omND0saHpY2svnf1z8aulhqebRcS0GTstNH0s96tIbPfALvcN/eDn2hZtqPCQ/FcSCorL\nsBAtgvgfFCREUTRrGxNj+rb20tmr38z9c/GrV7+Zq/1oD/dLiCZpt85gdrDrwlGNEEQE1DVlp3JS\nUlLYk91Lly598sknfdJYajRrGxM5eb52yR6XaqQ81LNQysZjd5W1n7tFbm6u9MsioyBJBa1Wq9Fo\ntFoBswMUFhZeuXKFeXjhwoVDhw75pLE0adY2RmwTREBaC6UmExQUgFYLGg1otVBQACaTENfx2F0V\n4Oc8yc7OlnIWOwJO2SHqwvJKcmj62DZjp4ltiArQ68FsBooCpp4ZUzjGYBDJJkTSqEuQMJedQ65e\nvbp+/XrmYXJycrdu3US0R1BC08de/Wbujfxv2LKkzmkuwTEYwGy+o0bMwcCBopijKj+XKeoSJAmq\nETNHx1TFZc5YLH7KOW21WnU6HfMwNzdXwTdqm7HTQtPG3ij4hi1L2dnZixYtEts0xeGwkCZFgV4P\n/vJtNqryc5miLkHyA2az2eTOLDm7OrvNQ7fWk3Q6ncHNaZBbt26Rg8TERJdlsZjGCqBZ2xh7WWrb\nvEFsuySP2ezeCtDdvn3XSbfWSnU6d6f4HLqr2vxcjqAg+ZiSkhKrw/vQfXzVD0PLli3Pnz/PPNyz\nhysCza3GcoQtSzfyv3lfWyW2RZKnpMSxxniAqL7tkxciQoCC5GNiY2MpivLghYz8ePZyPvTu3XvZ\nsmWDBw/u1KnTp59+WlhYGB4e7kHjioqKPXv2DBo0SCA7/QkjS288lt5fbGOkTmwsuOWczlRHAA/n\ncNctW7b07t07IiLC3RdKyM8LANLEtsE/0KohLi5Oyt0SHaIoyie9paamrl692ub4t99+i4mJAYDA\nwMAnn3zyww8/5LgcR+MjR47cd999/K/rc4T4KgVyDz/j23fhbW9GIw3g4C8vz5te3fXt++677/vv\nv3fWm5T9nBAXF0cDTRtp2uKj3iQMjpBURGJiYklJSWlpaVhY2L333gsAr776qk8aI4gDyMLPwIGg\n14PVChQF+flQUACsyAJf4bG7ysbPjQBmAB2AogPmcWOsVLBYLDRNCx1Zp9FoYmJiyI3nZeN58+a1\na9euTZs2U6ZM8amNiIIwGCAtDSwWoGmwWICihFAjglu+zf+FkvBzCgAArABGAC2AVTRDhEZdgoTb\nTXzFjRs3jh07duzYsR9++OHTTz/95ZdfxLbIK9AxEIe46+eXL1+eMmXK2LFj58+f39DQGLf5ySef\nLFmyZMmSJZcvX/bQjnwAY9OxFSAdQJB8FxJA7DlD/yHxNSTf8t13350+fdr+2CccOXJEo9HcuHGD\nPBw0aNDnn3/uh+sy4BqSLUYjnZ9PUxQNQFMUnZ9PG43e9yrNz8RdH+NeQ+LAAz83Go23bt2qra2d\nMGHCo48+WlVVNXXq1MOHD5NnP/roIw/MuPMtWGg6jaah6Y+iafe/ZGl+pwy4hqRMRo0a5fDYV4SG\nhrZq1YocBwcH19XV+ee6iANUlqHHnz7mlp8fOnTo2WefbdGiBQAsW7Zs0KBBJISvZ8+epEFaWtrx\n48c9341LAeQDmAFMANamGbwCgLymOT35o64pO8RXaDQasU1AmiCqI5kMPUrCLT8/f/58x44dmYcf\nf/zxyZMnDx8+zJyJiIi4cOGCtzbp7p7BK1DUDB4KEoLIHI4MPYgfGTx48Lp165iHs2fP/vHHH19/\n/fVt27aRM2vWrBkwYIAPrkQBGAAsTZuTrE3BDgU+6FtccMoOQWQOR4YexI8EBQW1bdt22bJlLVq0\n+Pnnn996661OnTr99NNPL730UmJiYkBAwOjRo4OCfPcvlwLIA1jWNFqyAqQ3xYVTPruIn9HQrpI7\nKYb4+HghyoEI1C3CgRCfuYy/R63WgfyQbAje7SKQ8WciHg0NDbdv3w4JCWGfrKysDAkJCQjwZEbK\n9bdgZckSAFBc25Uk/p3ilB2CyJy8PPfOI0ISEBBgo0YA0KJFC8/UiBdU0wweBQDy3q6EgoQgMqdp\nieIurFaBarMiEoVSwnYldQkS7n9EHCJvxzAYwGiE/HzbpKWC1QtHJArlJNiB8QItFJ0oAndKf/gZ\ndQmSBAv0IVJA9o7RlKEnPi4OaBry8xvPm81QUCCmYYj/oQDyWZuTrABGgHR5zOCpS5AQRBWkpTUu\nIFmtoNejJqkRnaPtSlaxrOELChLiFVVVVUeOHCkvLxfbEORudDowGgGaNAmjwD3ixo0bp0+fdvZs\nRUXFkSNHKioq/GmSG1BNM3gEK+spbdOfxEBBQjxnyZIlUVFRWVlZFEW98847YpuD3A1ZWwIAq9Xx\n5lnEFSaTadasWQ6feu+992JjYydMmNChQ4fFixf72TA3oOzOWFl/EgMFCfGQI0eOvPnmm3v37i0s\nLDx48GBubu7OnTvFNgq5m6wsSEsDaBonIbyZOXNm//79582b5/DZn376aeHChceOHdu/f//u3bun\nT5/+xx9/+NlCN6Ca/jjOSAMUJMRDDh06NHjw4K5duwJAbGxsly5dTp06JbZRyN1QFOTlNUbfmc2o\nSfwZPHjwO++8o3NSvWnHjh2DBg1q164dAHTr1q1fv34bN270k2Ua97MEWZr+KAAAoFhnJAYKEuIh\nzz333HfffUeOT5w4cezYseTkZHFNQhxA6rQymoSB4Px49NFHhw0bRn5v2RMeHn7mzBlyTNN0aWkp\n81BwSFS3Xn57jPiAgqR8LBbL77//LlzcwY4dOzIyMt5++23P8+ojgkI0iWA0KkmThPZtZzzzzDMH\nDx6cPn36rl27Jk+efPPmzaqqKj9dmwLIA9ABmO/eY6QIUJAUS01NzeTJk8PCwjp16pSQkBAeHj5m\nzBh3S6QHBwd//vnnzp69ffv2a6+99uyzzy5cuPDtt9/22mREMMjcHUH+m5P84NvcREVF7dixo7i4\nePr06XFxcSNHjiTTd/7DAJAPoAMwAuh5hydYID4uXoIzdQyY7VuZVFVVDRgw4OTJk3Pnzs3IyACA\n9evXz549e8iQIbt3777//vt9cpWnnnqqWbNmR48eve+++3zSISIgOh2UlIDR2BjgYJ/ZQSb4x7e5\nuXr1an19/cqVK8nDlJSUKVOm+OG6d0EBGAAGAugBCrgSqsoIHCEpk8WLFx84cKCgoODFF1/s1KlT\np06dpkyZsnDhwuLi4s8++8wnl1izZo3Vav3vf/+LauQ3Pv/88yeffHL48OHOvsTRN25wvd4mEFye\nm5P84NvOWLJkyY4dOwAgKCho2LBhBw4cAIBNmzYdPXp0xIgRgl7aKWmsoZL8UZcgyTtlGW9omp4z\nZ85TTz310EMPsc8/9dRTH3zwQVRUlFu93bp1a+LEieHh4W3bttXpdDdv3iTnf/rpp2PHjrVo0SK4\nidWrV/vsPfgXWTjGrl27fvzxxxUrVqxYseL777/fu3evbQurNefPP10sEbEDwWW4Ock/vu0Mg8Hw\n448/AkDr1q1nz579zDPPxMTEvPDCC2vWrGnZsqW778VnUAAGAGXUEaJVQ1xcnIy69YZz584BgNls\n9r6r5s2bt2/f/oknnli+fPm0adOaN2/+5ptvet+tlwjxmUvwe7Rh1apVq1evJsfTp09ftWqVfZs3\nIyNpANpo5OrIYqHT0mgAGoDW6TgaSvAzkZpvX7582XtLuPHttyDB75QNriEpELIfqGPHjj7pjaKo\n9evXA8C4ceOKi4u3bNnik24Rd3nqqafIwfnz53/55ZdXXnnFvs13oaE5EyeC2QwDBzaOhOwhAQ5k\nys5sBooCg2wWH6Tm2/5ZsvIQk/xWlVCQfIyVc16esltG9lV7+5a3b9/m6Jk/o0aNYo4TEhIOHjzo\nk26RioqKsrKymJgY5kx1dfXZs2fbtWsXGhpKzuzatWvTpk0A0Llz5wkTJgDA1q1bc3JyjEZjhw4d\nHPdL1IU7bIEEgmu1ANC4qsRHk7jXnOyv5av26NueYQQwA+Q1VaOQAyhIPmbZsmVGcoc7grYrGK/V\nciU45N/eaDQamv6nkDYOd+p9/fXX58+fnzZtGsdFbWD/BtRoVFTzXmgWLVpUXl6ek5NDHq5bt27W\nrFlRUVGlpaWZmZlvvPEGAERHR/fv3x8A2rRpAwA5OTmnTp1atmxZ+/btubrOyoKCAkhPd6FJeXmN\nuRu4R1QMy5aBc98Ge8fg9G032huNgL7tARYAPYBeTgF4KEg+JisrKysri397dzdPOGvPHiFFR0eH\nhYWtXbv2pZdesmn2/vvvx8fHu3VFxOcsWLBg9+7d+/fvHz16NDlTXl4+Y8aMTz75JDk5+fLly8OH\nD09NTU1JSYmNjY2NjSVtfv75Z6vV+umnn2o0Go7Oyfc7ecSIbBK2wOFgJC8OyQXOJxA8Kwvc8W2u\nS7vVHn3bMyiAfAATgBHO/fNcbpvc70K/E9smF6Ag+Rj7qTP/tw8ICJgyZcqsWbN+/fXXRx55hDm/\nZcuWw4cPT5061a0rIj4nJSUlMTFxw4YNzE/yvXv3RkZGktxLERERGRkZ27dvT0lJYb+KhDUy4cWv\nv/56mqMxTVFRUePR5Mmg1YJef2dLrD3szUncIypwNMnGjQDt0bfdxgCQBdHLonOMOTkTczKWZYht\nEBcoSMpk6tSpX3755ZAhQ+bOnTto0KDWrVtv3rx5ypQpDz/8sJ6VYbOqqqq4uLhDhw64l8ifJCUl\nAcCRI0eYFcGLFy+yZ+EiIyNLSkpsXjV79mz3LkMWilxOxJHZMEaT3B3W+B30bbeh7myhPdf8nNjW\ncKGufUjqISws7Lfffhs5cuS0adO6du3atm3bCRMmjB49et26dQEBjV86VjOSDnV1dYGBgczDoKCg\n2tpaH/TrUo0IsqpSgb7tIWlSTO9tA46QFEvr1q2/+uqrhoaGoqKi+vr6Ll26hISEMM+Sakb79+/v\n2rVrSUlJnz59HnvssdTUVJtOampq2A9nzJgxY8YMf1ivMoKDg6urq5mHVVVVwcHB/ru83ALB0beV\nCo6QFE5AQED37t179uzJvmMBqxlJjOjoaHZAv8VicRrVLRDsKhUyyQiOvq08UJBUClYzkhRJSUk1\nNTUrVqwAgKNHj27bti3d07w+nqdBYlepkHPlJPRth+Tm5ko/ChEFSe1gNSMp0KJFizlz5syfPz8l\nJSUzM3Py5Ml9+vTxrKvs7Gynz5GgOw6YKhVk7k7moG+zyc7OvhOBKVVwDUm93L59+x//+MfKlStz\nc3PHjBkjtjmqY+LEieyHGRkZv/7665UrV8LCwoKChLkxSXYG7iUidiB4XJwgZggP+rZMQUFSL1jN\nSGpoNJqIiAgBL8DOzsChSUwguGxB35YpKEgqhVQzOnDgADvaGFE+ZADkMlcQST50/rz/DPMd6Nvy\nBdeQVIqSqhkh7mEwgE7XmDHIGeyS53IDfVu+oCCplMWLF9fX19ewwKl2ZcAryi4rCyjKRdFYeRY4\nB/RtJ2CUneSQRWFQxP8oyTG4ouwYmAGQDIvGIp4hiyg7dQkSr3sVUR9qdAyy64i7ZBGC+Bd1CRKC\nIHegKAdFiRBEPFCQEARBEEmAYd/e0q9fP+kvFSqMfv36iW2CKkDflgKq8nYUJG9Zvny52CYgiI+w\nWtnBdba+TYpTFBQAAOh08o0LRySLWqbstFrtiRMntFqt2IYgiLB4HjGo1boIuiOxeUSx5Jx9VZ1g\n2DeCIP7G84hBkurbZfZVJiO4TKpUIAQM+0YQRD4QsXE59KGoO2XOzWYFJAVHpIPC15CYOTqm+hlz\nxmKRfDlfBPEzPLOvMs2sVjCZgKL41kpHEE4ULkjWu/f9WXEbIIJwwzP7KrtKhV5/p9osgniBsFN2\no0aNWrx4saCX4IZqwv6kOAYhikN0J/c9fLKvkmakRIXViimIEJ8grCANGDDgl19+aWhoEPQqHFia\nsFEgA8d0BIK4g+hOLghM9lWXzcgoymoFDGFFvEZDC5k75PLly//6178qKirGjh0bGRnJ1MHs3r27\ncBd1iFarZc/XURSl0+lQlhCG+Ph4z2KQpOPk4MW7cAAZ97hcaiXNyM2Fm5Mkjy89RACEXUP6f//v\n/+3btw8Atm/fzj4v1idCdMhoNFqtVrPZDDhUQrxGak7uM9jRdNzN8vMbNclsdlEfHUE4EVaQlixZ\nUldXBwANDQ3333//tWvXBL0cBxaLhf3TgGiS0WgE1CTEO6Tj5ITc3Fx/Jy8nmkSm7MiqEt5T0iM3\nN3fRokViW+ECYdeQQkNDT506NWnSpIyMjAceeOC5557bsmVLWFiYoBd1icFgIFIEAEaj0YSb+xAv\nkJqTi1NKg11h1mxuTC+ESAlZbIwVdoR04MABnU6XkZFhMplCQkL2798/a9asiooKPfducOExGAyx\nsbHEDBwnId4gWSf3NxgIjngPLSQvv/yywWBgn9mwYUPfvn0Fvagz4uLibM7ksRZgdTqdKFYhEsHe\nPXgicSf3JRRFWywu2hiNNAANwKsx4neE9RCvEXbKrqio6PHHH2efGTp06K1bt/78809Br8sTnU7H\n5Gswm82q+0mL+AKJO7nPIHF0fALBdbrG9rg5CXETYQWpbdu2JSUl7DPnzp0DgPDwcEGvyx+Kophd\nSmazGdOBI+4ifSf3DUxaVZfZVw2GO5uT8Ece4g7CCtKQIUPmzp27bds2sm3w5MmTr7322sCBA5s3\nby7odd2Coqj8/HyiSVar1WbHEoJwIwsn9w38s69ilQrEI4QNanjhhRdOnz798ssvBwUFNW/e/Nat\nWw8++OC7774r6EWdwTGFQjQpPT3darVardb09HRGohCEG0k5ueDwz76KgeCI+wibqYFQXFx85MiR\n6urqLl26JCYmCnSVzz//fO3atfX19aNGjXrxxRdtnrVarXFxcdHR0RxJvokUkeERe9iEqAEvd7D7\nx8ld4qd9+CYTmM2Ql+ciyTeTT4jM45G1JURUJJ6pQdgouyeffHLRokWCXoKwc+fOp59+urKy8ubN\nmyNGjNizZ499G61WS9KqWpwH/1gslrSme4y7JaIwPI4+8puT8yEuLm7hwoX+uJLRyCuOLi/vTtBd\nfr4f7EKcsXDhwri4OFVH2fkt7+SFCxeee+65e+6559577+3Vq9fZs2ft2zRr1iw/Px8AmGGQPRRF\n5eXlkZ1JZMBUgFv8EE6kllzVTxtjeWZf1enuZAR3mT4cERJZbIxVWnLV8+fPZ2ZmfvXVVx06dLB5\nioxVicwAAMeMnNVqXbZsGZEliqIMBoMOZxuUDiZXdRurle/WV5OpUZZ45sdDBEPiU3bCCtK4ceNI\n3kkbXH4iFRUVZWVlMTExzJnq6uqzZ8+2a9cuNDSUnNm1a9emTZsAoHPnzhMmTACArVu35uTk/OMf\n/8jIyLDvk/kmPNAkTA2ueDy+UT12ciGQ6L8bMjwikw1paY3h44gYSNRDmvBTclV3WbRoUXl5eU5O\nDnm4bt26WbNmRUVFlZaWZmZmvvHGGwAQHR3dv39/AGjTpg0A5OTknDp1atmyZe3bt+funAQs6PV6\njmg6MjCCpjSsmBoccYbHTq4iSGweyQheUAB6PVapQBwj6AqVB+u98+fPz8zMjIuLe/PNN8mZsrKy\n3r177969m6bpS5cu9evXb+fOnTav+umnn15++eWGhgaOnuOaIKu+JH7BpT1MGlYAMBqNbr0XRPow\nK72KCWoQ2wTnWCw0RTXGOOCtJBKS9hAJBjWkpKRMmjRpzJgxzJm9e/dGRkYmJycDQEREREZGhk3h\nGQD46aefjh07NmLEiOHDhw8fPtxZJEJRUVFRURFZ9SXjJJf2YGpwZUNWer2ZxJBaUINoaLUuknwz\nuR4AwGjEDbOIPcJO2U2YMKG0tPTll1/mv96blJQEAEeOHGEC4S5evMiehYuMjLTJ1AIAs2fP9q3l\nbDA1OMKBB06uQEiAg8sk3+x9tWYzDBzoYicTojJkUDG2rq4uMDCQeRgUFFRbW+srC3lCouxQkxB7\nFFsx1i2YVSKXVc9tqlRAk5jl5cG2bZjQQeVINKiBTXBwcHV1NfOwqqoqODjYyz6dYTKZnCmNTqdL\nS0sj2VdJpEMeLswiGNTAwNQydxmzYDCA2QxW613bkpgtTahJKkZYQWJCtL0hOjqavY/VYrF07drV\ns664qzubTCbuaDqSu4HsqzWbzQUFBRyJiBAZkZub6/FrfeLkCoFJYUdyBXHAZLojMDf4wIHCWYdI\nH0GCGlauXLljxw5yXF9ff/r06fr6evLw/Pnzb7/9tlu9JSUl1dTUrFixAgCOHj26bdu2dE/rrHBv\nYicbYM1mM0fkAqYGVyQeZDfwrZMrBzL55jJmweEtTFahEBUjiCBt2bLl0KFD5Pjq1at/+ctfysrK\nyMOysrJVq1a51VuLFi3mzJkzf/78lJSUzMzMyZMn9+nTx8cWN0E0iTuazkaTOBIRIQrGt07uQ7wZ\n7fkGki7IbOYKunN4y9hM4iE+JTc3Nz4+XmwrXCDslJ3HTJw4kf0wIyPj119/vXLlSlhYGBPFJBDM\nfljgnLvDchWINPFTLjtusrIaYxacBd1RlGPtwZtIMLKzs7OzsyWuScLuQ/IhGo0mIiJCaDUikL1H\nfMZJJDU4jpMQ5C7IGpLF4lRgHEY9kOk+RMXIRpB8Av/ZDJ6ahKnBlYH401zKg3uss22bg5OYEVz1\nqEuQ3JrNMBgMjN44g6KorKwsRpP0ej1qkhyRxDSXqjAYwGi8M6FHUXeqVHgasoQoAKFmwLZs2XLx\n4kUAqKysBIA5c+bcc889AHDt2jWBrigEOp3OZeEJoknQtDlJr9djanCVoAwnFw1yjzAbJ0je1YKC\nRk3CjOCqRBBBioqKOn/+fGFhIXnYtWvXY8eOMc96vItIsmBqcBWiNif3AWYzVxVzzAiOgMDZviWF\nH9LcYmpw+SLxLMg8ke67ICXPXVYxx4zgAiNdD6FpWuhs38pDy95ebgemBkcQx5CS5y5jFtgZwc1m\nMJsFNwyREuoSJC+DqUhgt0tNYnLcoSbJBYyyExwmpNtlzALT0moFk8lFSQtEWahLkLwMpmJKKHFr\nkk6nQ02SFxhl5w/I6IdJ8s0ByfUAGAiuOtQlSN7D1iSOnbA6nY7Ju2o0GvWYoQtBoEmTzGbX1flI\nXDhgILi6QEFyG0aTuLMzkNTgJJ+Q2WzmHlQhiFpIS+OVfRUAsrIay/fxGVQhigAFyRP4axKmBkcQ\nW/hkX4WmxSSyc5bPoAqRPyhIHuKZJmHKOwQBaBr9uKxfzg664zOoQmSOugTJt8FUjNhw12dCTZI+\nGGXnb/jnUWW3dDmoQmSOugTJ58FUJL+qy7qxmBpc4igpyk6B4opBd75AFvWQ1CVIQsCzDBKRLpIZ\nD1ODI8KhJHG9AwbdeU12dnZRUZHYVrgABcl/kJR3mBocQTyBHXSHmqTHAwcmAAAc7klEQVRQUJB8\nD3cJJZtyFbhtFkHAZAKt1o2gu4ICDHBQJChIPsZkMpnNZm5NYo+TuBsjiCowGECn45vpjmgSBt0p\nERQkH2MwGHQ6nUuZYWsSphdCkMbsq6T8BAc22Vdx0ltZoCD5Hnc1CTDlHYJ4ln0Vg+6UhboEyW8R\nsUSTXMoMpgaXCAoMlZYjnmVfdTmoQmSE2AWZ/If/K1ORAZDLSn15rB2CWNZPLCReuIwnSngX+fl8\nq/PpdI2l/ChKeLMUgsQ9RF0jJD9DJuVcDn0wNTiC3IF/9lWDAbOvKgwUJGFhNIm7GaYGR5A7MNlX\nucHsq4oDBUlwDAYDTdMum9mnBtdqtRqNBsUJUSMGA7jKyAWA2VeVBgqShLDRJMx3hyCuweyrCgIF\nSVqwNQlBEF5g9lWlECS2AYgt9rnAmVk7l2nFEUSlGAwAAEZjYyA43inyBEdIIsC9MmSjRlYWQhuG\nIBJFo8GS52pAXYIkkf2PZKDjTJOoJuzPC2yXepGIYyBOwZLn6kBdgiSRUjFM+XOtVms/7rE0Ya9A\nWK5CICTiGIhT3Mq+SsCgOxmiLkGSDowm8akeiyWUEASzr6oBFCTR4KlJ9mX9zC43DCKI8uCffZXk\negAMupMfKEhiwq1JFouFpmmy4MTWJJPJhGlYETWC2VeVDgqSyLA1ibsllvVD+KDwAA2iSXxiFrKy\nQKcDwJLnjeTm5sbHx4tthSvEze3qT6Sc5pYMhvjApMWjKApTg/sQKbsHf5TxLlyTl0fz+d9lsdBp\naY0ZwXU64c2SARL3EBwhSQL+Id04TkIQ0OmAR35IDASXHShI8gPLnyMIX2wCwTEgSNqgIEkU7vBu\nLH+OIHxhZ181mTAQXMqgIEkRk8mk1+ux/DmC+AbMvioTUJCkSFZWlk6nc7lEpNPpUJMQBAB4lZdl\nB4IjkgQFSYqQzbCoSQjCC7OZV6IgzL4qedQlSPLaosFfk/Kblm1RkzxDXo6B2MKUPMfsq3JH7Lhz\n/yHxAHxnkOAFl1uO2KWScH+SB8jUPWxQxrvwEKORpija5ZY+i6VxZxIArb47ReIeoq4RkhwhAXUu\nhz4URTGaZDQa9TgjgagNzL4qf1CQZACjSdzNiCaRPbZmsxk1CVEXmH1V/qAgyQODwUDz2JpOMuOh\nJiEqxePsq4g0QEFSGjaaxFErHUEUiFvZV5mgO7xNpAEKkgJha5LVakVNQtRFWhoYjWAwuGhGpvgw\nEFxKoCApE9QkRNW4VCMCBoJLDBQkuaLRaLiXiOw1yWWtdARRHTZBd5h9VVRQkOSKxWJxuURko0nc\ntdIRRKUw4XlWK2ZfFRcUJLnCbDxCTUIQF7gVdIeB4OKBgiRjmPLn3NNxpFlaWhqgJiEqxGrltT6E\n2VclAAqSvGE0iVtmKIrKy8tDTULUCJmRw+yrcgAFSfagJiGICzD7qkxAQVICbE3ibpaXl8eUP0dN\nQlSEwQA6nev1IZuS56hJ/gUFSSEQTWLn/HbWLCsri61J3LXSEUQ58M++ypQ8x+yr/gUFSTmQUDo+\nzdiapNfrUZMQVcA/+yoG3YmEugQJ67ARUJNsQMdQC/yzr2LQnRioS5Cys7PFNsGvcMgMqZLO1iSz\niveoq80xVA0ZJzGTchywg+5Qk/yCugRJbbgc+rA1yWQyYflzRBXodLyasYPuCgowENwPoCApFqvV\nqtPp9Ho9t8ywNclsNqMmIcgdyBQfBoL7iyCxDUCEgiwUAQCZizM4z39MnjIajUSTuBsjiLogmkQS\ndJnNMHBg4zweIgA4QlIyZKFIp9O5HPrgOAlBnMLOvqrXYyC4cKAgKR+iSUajkb8muWyMiMJHH300\nfPjwxx57bPny5WLboiC0Wrezr2q1oNGAVgsFBTiP50to1RAXFye2CWJCxMZoNPJpRnDZWElI3z1+\n/fXXcePG1dTUXLlyJSkpyWKx2LeR/ruQIhYLDUDz8XaKogHu/DEP5XOnSNxDcA1JLTALReBqPSk2\nNpaU/nPZGPEnGo1m0qRJzZs3Dw8Pb9euHU3TYlukFMiMHBkkcXs7s5hEYDbMDhwolG0qAwVJRRBp\ncSkwOp0OAFCTpEZycjIArF+//uuvv3744YexLL0v0emgpMR1zILD3UgUBXo9uMrahfABBUld8JQW\n1CQ/UFFRUVZWFhMTw5yprq4+e/Zsu3btQkNDyZldu3Zt2rQJADp37jxhwgQAePDBB++5554PP/zw\n0KFDvXv3FsVyZUI8XK+/E+dtj8McQphYyHdgUAPiGJ1Ox6RqxRgHIVi0aNHixYuZh+vWrRswYMDr\nr7+enp7+f//3f+RkdHR0//79+/fv37Nnz4KCguLi4g4dOgwaNOjpp5/evHmzSIYrFyb7qjMcChVF\nORUwxE1QkBCnMFXSAcBoNOpxp7qPWLBgwf/8z//ksbLXlJeXz5gxY9GiRWvXrt24ceOqVat27doF\nALGxsUOGDBkyZEhCQsLRo0c//fRTsnR07Nixtm3bOuw8Pj4+Pj4es/N5gsvsq84SDvFJRCQeubm5\n8U2IbYsLUJBUjUaj4ZYZtiaZzWbUJJ+QkpIyadKkMWPGMGf27t0bGRlJVokiIiIyMjK2b99u86oJ\nEyacP39+2LBhI0eOrKysfPbZZx12XlRUVFRUhNn5PIRsg3W202jbNgcnJV9eNjs7u6gJsW1xAa4h\nqRqLxaLVaq1Waz5TlMwOokmkmh/J45An7d+D0icpKQkAjhw5whRIvHjxYvv27ZkGkZGRJSUlNq9q\n1arVF198UVFRERgYeM899/jLWPVBUeAsgpGsMw0ceKcmRVoaFBQ0ahLeF16DIyRVQ8TGarVyh2yR\n6n+k3hKOk4Sgrq4uMDCQeRgUFFRbW+uw5b333otqJCYGA6SlgcUCNA00jSXPfQsKktphyp+7pUkY\nc+xbgoODq6urmYdVVVXBwcEi2oPwhV3yHMvLeg0KEnKXJlmdx7CyNcnloApxi+joaPYnb7FYOnTo\nIJ45yN3wLHmO5WW9BgUJAWBpElkr4m6GmuRzkpKSampqVqxYAQBHjx7dtm1buqcV4TC+zsdote6V\nPE9Pl6YmkVg7sa1wAQoS0ghbk1w2Y2sSh4AhPGnRosWcOXPmz5+fkpKSmZk5efLkPn36eNYVxtf5\nGDIj53LdNCurse6fVIPuSKyd2Fa4Quxkev5D4lkFJYLDlJ0Om1FNmwFJZISwZgmPFNyjoaHh0qVL\ntbW1HvcghXehQHhmX7VY6LS0xnSrOp1fLHMbiXsIjpCQu6D47Tm3GSdxT/QhPNFoNBEREUFBuBlD\nYpBVIqPRRRwdu+Q5Bt15BAoS4iFEk9LS0gA1CVE8ZJXIZRwdBt15h3IECWuX+R+KovLy8mw0SavV\najQajHdAlAbZgeQyjg6D7rxAIYK0e/fuXbt2rV69+ssvv8zNzcWf6j5Eq9UWOP+hZ69JfjMMcQhG\n2QmIweAi+yrBJuhOGmCUnf/A2mUCYbVadTqdXq8nSYMcQjSJKX+OvwbEBaPsBIQZ/bgkK6uxrpJk\ngu5kEWWnkOVTrF0mEBRFZWVlAYDJZCopKXFWFYmiKHbtcwLzLViwdhmiGCiKVy0+Il1kT5LZDBTl\nohYtAgCSFSSsXSYdKIoiOkQGSTwr9eE4CVE7JMCB/CwjP9dQk1whUUFatGhReXl5Tk4Oebhu3bpZ\ns2ZFRUWVlpZmZma+8cYb0FS7DADatGlTUFAQExPTuXPnDh06nD17dvPmzShIvsWlJjHx4mwp4hlE\njiDKhGgSWUZyWR8dkaAgLViwYPfu3fv37x89ejQ5Q2qXffLJJ8nJyZcvXx4+fHhqampKSkpsbGxs\nbCxps3jx4o0bN77//vsajebYsWM9e/YU7x0oFqJDziqaM/NyNrkbsFYFomrS0sBoBKOxcTGJoz46\nIsGgBkFrl2ExTS8xGAxGo5F/RXOr1arX66Vc/pwppim2IYhs0WpdxHYbDBIMupMmkhshCVq7TPpB\nJtKHjI1criRRFKXT6YxGI1PWj+fik5/Jzs4mYWmoSYgnkH9T6ekuIh2ysqCgAEv5uURyIyR7sHaZ\n1OCWFpLXzmKxkOEUABBNkvI4SUngBIBfIatELmO7JZBVCPch+QasXSZfUJP8D+5D8jckENylzLCz\nCpEsRP5FFvuQZCBIPqxdhj8e/Y8sNAkdA/EKt7KvEkwmzHRnjwwEyYe1y/DHoxBoNBo953wFW5P4\nB0T4E3QMxFt4Zl9lZxXCTHd2SC6owR5Su2z69OkLFy68efOmN7XLECGwWCwkKQNHhDc7ZNxZ4DiC\nyJusLF6x3cTzSSC4y2gItSFyPSbeYO0yKUM2IVEUxd2MnV7I6LLcmX9Rhnso413IGFKjz9WNIGIp\nP4l7iAym7AhYu0zKkKKxwMpf5xCDwcCMoqQ5d4cgXkFWiVwOeiQQdCdNZCNIPgHXroWD1OsDV5qk\n0+kkqEnoGIjP4JmIAUv5OUJdgoRr14LC1iSO5KoS1CQlOQaKq2zwbyk/3IeEqA5Gk7gjISWoSYpB\nSeKqfGxK+QmpSbgPCVEjjCZxo9PpmHysqEmIYtFqXUzHGQyg0wFgpjsAFCRECJgYB/7NUJMQBWK1\nAkW5no4zGKRWXlYsUJAQMbHRJO4NtggiM5hVIu6hDwbdNaEuQcL1XgnC1iSz2SyKJqFjIELBP/sq\nBt2pTZBwvVcstFptgfN7jGgSKS8riiahYyACQsSGT/ZVPwbdSRN1CRIiClarVafT6fV6bk3Kz88X\nUZMQREDS0nhlX7UJulMfKEiI4FAUlZWVRTSJI3LBRpO4N9giiMzgmX01K+tOgIP6NAkFCfEHjCZx\nV6Bga5LVakVN8gBcD5MuRGy4p+PYAQ4FBT4McJDFxlgNTdNi2+An4uPjpb8vTPGYTCaz2azT6Tiy\nfVut1vT0dJLrgWcEufcowz2U8S6UDAkE59OM+TVmNILvUuNL3EPUNULCH4+iYzAYJDhOQsdA/ARm\nuuNEXYKEwVRSgGgS905Ye03iSI7nPegYiORIS1NhKT91CRIiEUgNWe4afTaaxEziIYhaMBjUFnSH\ngoSIA5+KsahJiPLhH3Sngr0QKEiIpCGalJaWBqhJiPIwmdwIulNBViEUJETqUBSVl5eHmoQokKws\noCgXhSfYAQ4ut9bKHBQkRCpwxzigJiEKxK3sqwRFB92hICGSoKCggDvbN2oSokx4Zl9lZxVSbtCd\nugQJt5tIlrS0NIvFwp3FjmiS0WgEX2sSOgYiJjyzr6oh6I5WDXFxcWKbgLiAJGWgKIq7DdEkaMrj\n4JNLK8M9lPEuVEpeHg1AG41cbSwWOi2NBqABaJ3Og4tI3EPUNUJCJA6TKIgjOwNJi8ceJ3EkEVch\nONqTK3yyr3oRdCeLXHYoSIi0IHHe4I4mcRe2UBuYdULGkKA7svHIGTZZhcxmnn1nZ2dLOYsdAQUJ\nkRxsTXK2SoSahCgQtthwN2NK+ZlMSgpwQEFCpAijSZTzZJQURZEURICahKgNm1J+StEkFCREovAs\nPGGjSWbeMxgIIm8MBtDpABQVdIeChMgetiaZTCaODbYIIjNcBoIrK9MdChKiBNiaxF1sCUFkg8kk\nXNCdNEFBQmQDd1Uk1CREaZBJOZfZVxVUyk9dgoRbNOSL1WpNS0vj3nXksSahYyAShWf2VSboTu5Z\nhcTemes/JL5FGXEJydFAAvA4mrHzOBi5972zUIZ7KONdIHdhsdAURXOmL6FpmjYaGzM4cLaUuIeo\na4SEyBqy90in0+n1eo7RD3ucxF0oHUFkAM/sq+xSfrINukNBQuQEo0ncM3KMJgEAahIie/hkX2UH\nOBQUyDTAIUhsAxDEPch+WAAgW46clUI3GAyxsbEkdzgRJz5F0xFEoqSlgdHYuBnWmScT3SI5t7hb\nShUUJESW8NEknU4HAKhJiEIg3ms2c8kM0SQyZWc2w8CBLjLjSQycskPkisFg0Ol03Bqj0+nymkpt\n4twdInsMBnCZvoSMpUCWQXcoSIiM4TPiQU1CVIdsS/mhICHKR6fTMWnxFK9JuKcKAbg76E6vB6yH\nhCDSgZ2qVdmahPWQEAAHWYWwHhKC+BsOpbHRJL0iklEiqkajcREIzmQVMhrBZAKttujECdBqJRsX\njoKEKAez2cytNGxNMpvNqEmIvOFZ8pxgNt8JcEhPb5QoiaEuQcLpdWVD1oq4lYZoEqn7x7REx0Bk\nCZ/sq+xSfgTmYOBAAW3zCA1N02Lb4Cfi4+OlP4WKeI/VatVqtezgOodt0tPTSe5w0rJ58+a1tbU8\nqwJKFnRy1cHEdufng7PyylqtA8UijSXm7eoaISFqgIiK2WzWki3rTtrk5+cz46R0WYXGIsgdmEk5\nDh92OH6yWiW4RQkFCVEgzECHpyYVFBTU1tb6zTwE8SUus686HDlRlNMRlXigICHKhOgNcJb1oyjK\n/iltEwIbiCC+g4yTnGVfdTZ37XxOWywwlx2iWIgmpaenU7x/CXJUpEUQSaPTQUmJ40x327Y5aC/J\nKTsMakBUDTMSYqSIUS85RjegkyOOMZlg4MDG8AcyxVdQADqd2GbZgoKEIAAAGGWHqAGJewiuISEI\ngiCSAAUJURccMQ4IgogLChKiLiiKSk9PL7DLtqLVammalvV8HYLcBXemO0mCgoSoi7y8PJ1Op9fr\n7TUJQRRFXp40E9ZxgGHfiLqgKCorKwsA9Hp9Xl5emqwKPCOIGzCB4PIpZI6ChKgOtia5LIKOIDKG\n+LZez5XpTkrglJ1ikWMGa7/ZTFHUzZs3dTqd2WxWcLE+xYNO7vpaWVlAUXIpZI6CpFgWLVoktglu\n40+b161bZzAYUJNkDTq562vxyb4qGVCQfI8PfwH5+8eUj5pxt/HsTTl8lZcnAYBokpEUjEF4g04u\nIye/k5pB8hUpVZSpYfz48Xv37hXbCkSi9OvXb/ny5WJb4S3o5IgzRt+4kfPnn7lPPZW9apXYtjhF\nRYKEIAiiagoKJB5uh4KEIAiCSAJcQ0IQBEEkAQoSgiAIIglQkBAEQRBJgIKEIAiCSAIUJARBEEQS\noCAhCIIgkgAFSVFUVFScPXuWfaa6uvrkyZM3btwQyySXOLRQCLNv3bp14sSJmzdvCn0hRFDQyTmQ\nvZPTiIJ4//3333zzTebh999/37dv35EjRyYkJMyZM0dEw5z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      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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2bNi9e3c+nz948KDzgMOHD+fz+S9cMz09Hf0ggYjVboWkVja+9zJ9hzTXIkkf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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%% Non-empty Dirichlet boundary condition.\n",
    "pde = sincosdata3;\n",
    "mesh.bdFlag = setboundary3(node,elem,'Dirichlet','~(x==0)','Neumann','x==0');\n",
    "femPoisson3(mesh,pde,option);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pure Neumann boundary condition\n",
    "\n",
    "When pure Neumann boundary condition is posed, i.e., $-\\Delta u =f$ in $\\Omega$ and $\\nabla u\\cdot n=g_N$ on $\\partial \\Omega$, the data should be consisitent in the sense that $\\int_{\\Omega} f \\, dx + \\int_{\\partial \\Omega} g \\, ds = 0$. The solution is unique up to a constant. A post-process is applied such that the constraint $\\int_{\\Omega}u_h dx = 0$ is imposed. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Multigrid V-cycle Preconditioner with Conjugate Gradient Method\n",
      "#dof:     6528,  #nnz:    24957, smoothing: (1,1), iter: 20,   err = 7.43e-09,   time = 0.092 s\n",
      "Multigrid V-cycle Preconditioner with Conjugate Gradient Method\n",
      "#dof:    50688,  #nnz:   198141, smoothing: (1,1), iter: 21,   err = 4.01e-09,   time = 0.24 s\n",
      "Multigrid V-cycle Preconditioner with Conjugate Gradient Method\n",
      "#dof:   399360,  #nnz:  1579005, smoothing: (1,1), iter: 22,   err = 4.23e-09,   time =  2.7 s\n",
      "Table: Error\n",
      " #Dof        h        ||u-u_h||    ||Du-Du_h||   ||DuI-Du_h|| ||uI-u_h||_{max}\n",
      "\n",
      "   864   2.500e-01   2.24448e-02   5.86299e-01   1.53064e-01   6.19341e-02\n",
      "  6528   1.250e-01   5.72292e-03   2.94670e-01   5.84934e-02   1.63182e-02\n",
      " 50688   6.250e-02   1.43932e-03   1.47567e-01   2.66183e-02   4.13880e-03\n",
      "399360   3.125e-02   3.60390e-04   7.38135e-02   1.29661e-02   1.03857e-03\n",
      "\n",
      "Table: CPU time\n",
      " #Dof    Assemble     Solve      Error      Mesh    \n",
      "\n",
      "   864   4.00e-02   1.86e-03   2.00e-02   1.00e-02\n",
      "  6528   3.00e-02   9.16e-02   3.00e-02   1.00e-02\n",
      " 50688   2.10e-01   2.37e-01   1.30e-01   7.00e-02\n",
      "399360   2.74e+00   2.70e+00   1.41e+00   0.00e+00\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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CnKChoWHLli0//PBDVVVVv379Bg4c+Ne//rVFCCwEETXYyXlE+oKUtdeY2KerZvM50+/1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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%% Pure Neumann boundary condition.\n",
    "option.plotflag = 0;\n",
    "mesh.bdFlag = setboundary3(node,elem,'Neumann');\n",
    "femPoisson3(mesh,pde,option);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Robin boundary condition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Multigrid V-cycle Preconditioner with Conjugate Gradient Method\n",
      "#dof:     6528,  #nnz:    24960, smoothing: (1,1), iter: 17,   err = 3.83e-09,   time = 0.074 s\n",
      "Multigrid V-cycle Preconditioner with Conjugate Gradient Method\n",
      "#dof:    50688,  #nnz:   198144, smoothing: (1,1), iter: 17,   err = 7.40e-09,   time = 0.31 s\n",
      "Multigrid V-cycle Preconditioner with Conjugate Gradient Method\n",
      "#dof:   399360,  #nnz:  1579008, smoothing: (1,1), iter: 17,   err = 7.34e-09,   time =    3 s\n",
      "Table: Error\n",
      " #Dof        h        ||u-u_h||    ||Du-Du_h||   ||DuI-Du_h|| ||uI-u_h||_{max}\n",
      "\n",
      "   864   2.500e-01   1.70968e-02   5.78078e-01   1.24451e-01   2.87371e-02\n",
      "  6528   1.250e-01   4.51894e-03   2.93659e-01   5.40040e-02   7.24170e-03\n",
      " 50688   6.250e-02   1.14572e-03   1.47441e-01   2.60230e-02   1.82017e-03\n",
      "399360   3.125e-02   2.87439e-04   7.37977e-02   1.28910e-02   4.57164e-04\n",
      "\n",
      "Table: CPU time\n",
      " #Dof    Assemble     Solve      Error      Mesh    \n",
      "\n",
      "   864   5.00e-02   9.15e-04   0.00e+00   0.00e+00\n",
      "  6528   3.00e-02   7.44e-02   2.00e-02   1.00e-02\n",
      " 50688   2.00e-01   3.09e-01   1.70e-01   7.00e-02\n",
      "399360   2.16e+00   3.05e+00   1.48e+00   0.00e+00\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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ycUFBQlygvr5+7dq133//fVVVVWJiYu/evR999FGrEFgI4tdgJxcR+QtS7lbLsO7t9Wt+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\nWlo6ffp01+7opxBNIstIZOJOjBRi3gCdGhAJQeKr6nQ6/oh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      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%% Pure Robin boundary condition.\n",
    "pde = sincosRobindata3;\n",
    "mesh.bdFlag = setboundary3(node,elem,'Robin');\n",
    "femPoisson3(mesh,pde,option);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion\n",
    "\n",
    "\n",
    "The optimal rate of convergence of the H1-norm (1st order) and L2-norm (2nd order) is observed. No superconvergence for $\\|\\nabla u_I - \\nabla u_h\\|$.\n",
    "\n",
    "MGCG converges uniformly in all cases."
   ]
  }
 ],
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    {
     "text": "MetaKernel Magics",
     "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
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   ],
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